# Electronvolt

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In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. When used as a unit of energy, the numerical value of 1 eV in joules (symbol J) is equivalent to the numerical value of the charge of an electron in coulombs (symbol C). Under the 2019 redefinition of the SI base units, this sets 1 eV equal to the exact value 1.602176634×10−19 J. [1]

## Contents

Historically, the electronvolt was devised as a standard unit of measure through its usefulness in electrostatic particle accelerator sciences, because a particle with electric charge q gains an energy E = qV after passing through a voltage of V. Since q must be an integer multiple of the elementary charge e for any isolated particle, the gained energy in units of electronvolts conveniently equals that integer times the voltage.

## Definition and use

An electronvolt is the amount of kinetic energy gained or lost by a single electron accelerating from rest through an electric potential difference of one volt in vacuum. Hence, it has a value of one volt, 1 J/C, multiplied by the elementary charge e = 1.602176634×10−19 C. [2] Therefore, one electronvolt is equal to 1.602176634×10−19 J. [1]

The electronvolt (eV) is a unit of energy, but is not an SI unit. It is a common unit of energy within physics, widely used in solid state, atomic, nuclear, and particle physics, and high-energy astrophysics. It is commonly used with SI prefixes milli-, kilo-, mega-, giga-, tera-, peta- or exa- (meV, keV, MeV, GeV, TeV, PeV and EeV respectively). The SI unit of energy is the joule (J).

In some older documents, and in the name Bevatron, the symbol BeV is used, where the "B" stands for billion. The symbol BeV is therefore equivalent to the GeV.

## Relation to other physical properties and units

MeasurementUnitSI value of unit
Energy eV1.602176634×10−19 J
Mass eV/c21.78266192×10−36 kg
Momentum eV/c5.34428599×10−28 kg·m/s
Temperature eV/kB1.160451812×104 K
Time ħ/eV6.582119×10−16 s
Distance ħc/eV1.97327×10−7 m

### Mass

By mass–energy equivalence, the electronvolt corresponds to a unit of mass. It is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum (from E = mc2). It is common to informally express mass in terms of eV as a unit of mass, effectively using a system of natural units with c set to 1. [3] The kilogram equivalent of 1 eV/c2 is:

${\displaystyle 1\;{\text{eV}}/c^{2}={\frac {(1.602\ 176\ 634\times 10^{-19}\,{\text{C}})\times 1\,{\text{V}}}{(299\ 792\ 458\;\mathrm {m/s} )^{2}}}=1.782\ 661\ 92\times 10^{-36}\;{\text{kg}}.}$

For example, an electron and a positron, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. A proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, which makes the GeV/c2 a convenient unit of mass for particle physics: [4]

1 GeV/c2 = 1.78266192×10−27 kg.

The atomic mass constant (mu), one twelfth of the mass a carbon-12 atom, is close to the mass of a proton. To convert to electronvolt mass-equivalent, use the formula:

mu = 1 Da = 931.4941 MeV/c2 = 0.9314941 GeV/c2.

### Momentum

By dividing a particle's kinetic energy in electronvolts by the fundamental constant c (the speed of light), one can describe the particle's momentum in units of eV/c. [5] In natural units in which the fundamental velocity constant c is numerically 1, the c may informally be omitted to express momentum as electronvolts.

${\displaystyle E^{2}=p^{2}c^{2}+m_{0}^{2}c^{4}}$

in natural units (with ${\displaystyle c=1}$)

${\displaystyle E^{2}=p^{2}+m_{0}^{2}}$

is a Pythagorean equation. When a relatively high energy is applied to a particle with relatively low rest mass, it can be approximated as ${\displaystyle E\simeq p}$ in high-energy physics such that an applied energy in units of eV conveniently results in an approximately equivalent change of momentum in units of eV/c.

The dimensions of momentum units are T−1LM. The dimensions of energy units are T−2L2M. Dividing the units of energy (such as eV) by a fundamental constant (such as the speed of light) that has units of velocity (T−1L) facilitates the required conversion for using energy units to describe momentum.

For example, if the momentum p of an electron is said to be 1 GeV, then the conversion to MKS system of units can be achieved by:

${\displaystyle p=1\;{\text{GeV}}/c={\frac {(1\times 10^{9})\times (1.602\ 176\ 634\times 10^{-19}\;{\text{C}})\times (1\;{\text{V}})}{2.99\ 792\ 458\times 10^{8}\;{\text{m}}/{\text{s}}}}=5.344\ 286\times 10^{-19}\;{\text{kg}}{\cdot }{\text{m}}/{\text{s}}.}$

### Distance

In particle physics, a system of natural units in which the speed of light in vacuum c and the reduced Planck constant ħ are dimensionless and equal to unity is widely used: c = ħ = 1. In these units, both distances and times are expressed in inverse energy units (while energy and mass are expressed in the same units, see mass–energy equivalence). In particular, particle scattering lengths are often presented in units of inverse particle masses.

Outside this system of units, the conversion factors between electronvolt, second, and nanometer are the following:

${\displaystyle \hbar =1.054\ 571\ 817\ 646\times 10^{-34}\ \mathrm {J{\cdot }s} =6.582\ 119\ 569\ 509\times 10^{-16}\ \mathrm {eV{\cdot }s} .}$

The above relations also allow expressing the mean lifetime τ of an unstable particle (in seconds) in terms of its decay width Γ (in eV) via Γ = ħ/τ. For example, the
B0
meson
has a lifetime of 1.530(9)  picoseconds, mean decay length is = 459.7 μm, or a decay width of (4.302±25)×10−4 eV.

Conversely, the tiny meson mass differences responsible for meson oscillations are often expressed in the more convenient inverse picoseconds.

Energy in electronvolts is sometimes expressed through the wavelength of light with photons of the same energy:

${\displaystyle {\frac {1\;{\text{eV}}}{hc}}={\frac {1.602\ 176\ 634\times 10^{-19}\;{\text{J}}}{(2.99\ 792\ 458\times 10^{10}\;{\text{cm}}/{\text{s}})\times (6.62\ 607\ 015\times 10^{-34}\;{\text{J}}{\cdot }{\text{s}})}}\thickapprox 8065.5439\;{\text{cm}}^{-1}.}$

### Temperature

In certain fields, such as plasma physics, it is convenient to use the electronvolt to express temperature. The electronvolt is divided by the Boltzmann constant to convert to the Kelvin scale:

${\displaystyle {1\,\mathrm {eV} /k_{\text{B}}}={1.602\ 176\ 634\times 10^{-19}{\text{ J}} \over 1.380\ 649\times 10^{-23}{\text{ J/K}}}=11\ 604.518\ 12{\text{ K}},}$

where kB is the Boltzmann constant.

The kB is assumed when using the electronvolt to express temperature, for example, a typical magnetic confinement fusion plasma is 15 keV (kiloelectronvolt), which is equal to 174 MK (megakelvin).

As an approximation: kBT is about 0.025 eV (≈ 290 K/11604 K/eV) at a temperature of 20 °C.

### Wavelength

The energy E, frequency v, and wavelength λ of a photon are related by

${\displaystyle E=h\nu ={\frac {hc}{\lambda }}={\frac {4.135\,667\,516\times 10^{-15}\,\mathrm {eV{\cdot }s} \times 299\,792\,458\,\mathrm {m/s} }{\lambda }}}$

where h is the Planck constant, c is the speed of light. This reduces to [6]

{\displaystyle {\begin{aligned}E\mathrm {(eV)} &=4.135\,667\,516\times 10^{-15}\,\mathrm {eV{\cdot }s} \times \nu \\[4pt]&={\frac {1\ 239.841\ 93\,{\text{eV}}{\cdot }{\text{nm}}}{\lambda }}.\end{aligned}}}

A photon with a wavelength of 532 nm (green light) would have an energy of approximately 2.33 eV. Similarly, 1 eV would correspond to an infrared photon of wavelength 1240 nm or frequency 241.8 THz.

## Scattering experiments

In a low-energy nuclear scattering experiment, it is conventional to refer to the nuclear recoil energy in units of eVr, keVr, etc. This distinguishes the nuclear recoil energy from the "electron equivalent" recoil energy (eVee, keVee, etc.) measured by scintillation light. For example, the yield of a phototube is measured in phe/keVee (photoelectrons per keV electron-equivalent energy). The relationship between eV, eVr, and eVee depends on the medium the scattering takes place in, and must be established empirically for each material.

## Energy comparisons

EnergySource
5.25×1032 eVtotal energy released from a 20  kt nuclear fission device
12.2 R eV (1.22×1028 eV)the Planck energy
10 Y eV (1×1025 eV)approximate grand unification energy
~624 E eV (6.24×1020 eV)energy consumed by a single 100-watt light bulb in one second (100 W = 100 J/s6.24×1020 eV/s)
300 E eV (3×1020 eV = ~50  J )The first ultra-high-energy cosmic ray particle observed, the so-called Oh-My-God particle. [10]
2 PeVtwo petaelectronvolts, the highest-energy neutrino detected by the IceCube neutrino telescope in Antarctica [11]
14 TeVdesigned proton center-of-mass collision energy at the Large Hadron Collider (operated at 3.5 TeV since its start on 30 March 2010, reached 13 TeV in May 2015)
1 TeVa trillion electronvolts, or 1.602×10−7 J, about the kinetic energy of a flying mosquito [12]
172 GeVrest energy of top quark, the heaviest measured elementary particle
125.1±0.2 GeVenergy corresponding to the mass of the Higgs boson, as measured by two separate detectors at the LHC to a certainty better than 5 sigma [13]
210 MeVaverage energy released in fission of one Pu-239 atom
200 MeVapproximate average energy released in nuclear fission fission fragments of one U-235 atom.
105.7 MeVrest energy of a muon
17.6 MeVaverage energy released in the nuclear fusion of deuterium and tritium to form He-4; this is 0.41 PJ per kilogram of product produced
2 MeVapproximate average energy released in a nuclear fission neutron released from one U-235 atom.
1.9 MeVrest energy of up quark, the lowest mass quark.
1 MeV (1.602×10−13 J)about twice the rest energy of an electron
1 to 10 keVapproximate thermal temperature, ${\displaystyle k_{\text{B}}T}$, in nuclear fusion systems, like the core of the sun, magnetically confined plasma, inertial confinement and nuclear weapons
13.6 eVthe energy required to ionize atomic hydrogen; molecular bond energies are on the order of 1 eV to 10 eV per bond
1.6 eV to 3.4 eVthe photon energy of visible light
1.1 eVenergy ${\displaystyle E_{g}}$ required to break a covalent bond in silicon
720 meVenergy ${\displaystyle E_{g}}$ required to break a covalent bond in germanium
< 120 meVapproximate rest energy of neutrinos (sum of 3 flavors) [14]
25 meV thermal energy, ${\displaystyle k_{\text{B}}T}$, at room temperature; one air molecule has an average kinetic energy 38 meV
230 μeVthermal energy, ${\displaystyle k_{\text{B}}T}$, of the cosmic microwave background

### Per mole

One mole of particles given 1 eV of energy each has approximately 96.5 kJ of energy – this corresponds to the Faraday constant (F96485 C⋅mol−1), where the energy in joules of n moles of particles each with energy E eV is equal to E·F·n.

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